Date: Oct 29, 2014, time: 11:15
Abstract. In 1966, Arnold proposed to look at Euler’s equation for perfect ﬂuids as describing the geodesic ﬂow of volume preserving diﬀeomorphisms. In the same spirit, in 1989 Brenier designed a least action principle based on optimal quadratic transport which allows for getting rid of the high regularity assumptions which underly Arnold’s approach. Replacing deterministic geodesics on the state space by sample paths of Brownian bridges and optimal transport by minimal entropy, we obtain a least action principle for the Navier-Stokes equation, very much in the spirit of Brenier’s representation of the Euler equation. This is a joint work with M. Arnaudon, A.-B. Cruzeiro and J.-C. Zambrini.